Explosive character of instability development for the free surface of a conducting liquid in an electric field

Abstract

In this work, a perfectly conducting liquid with a free surface, placed in an external uniform electric field, is considered. For a symmetric spatially localized perturbation of the surface, which is directed upwards, it is proved that the part of the potential energy functional which is responsible for nonlinear wave interactions is negatively defined. It is important that this result is obtained without any restrictions on the amplitude of the boundary perturbations, i.e., it takes into account high-order nonlinearities. A general conclusion is that the nonlinearity plays a destabilizing role accelerating the linear instability development of the boundary and defining its explosive character.